Venezuelans are voting in a referendum Sunday to supposedly decide the future of a large swath of neighboring Guyana that their government claims ownership of, arguing the territory was stolen when a north-south border was drawn more than a century ago.

Guyana considers the referendum a step toward annexation, and the vote has its residents on edge. It asks Venezuelans whether they support establishing a state in the disputed territory known as Essequibo, granting citizenship to current and future area residents, and rejecting the jurisdiction of the United Nations’ top court in settling the disagreement between the two South American countries.

“We are solving through constitutional, peaceful and democratic means an imperial dispossession of 150 years,” President Maduro said after voting in a military complex in Caracas, the capital.

The International Court of Justice on Friday ordered Venezuela not to take any action that would alter Guyana’s control over Essequibo, but the judges did not specifically ban officials from carrying out Sunday’s five-question referendum. Guyana had asked the court to order Venezuela to halt parts of the vote.

The legal and practical implications of the referendum remain unclear. But in comments explaining Friday’s verdict, international court president Joan E. Donoghue said statements from Venezuela’s government suggest it “is taking steps with a view toward acquiring control over and administering the territory in dispute.”

“Furthermore, Venezuelan military officials announced that Venezuela is taking concrete measures to build an airstrip to serve as a ‘logistical support point for the integral development of the Essequibo,’” she said.

The 61,600-square-mile territory accounts for two-thirds of Guyana and also borders Brazil, whose Defense Ministry earlier this week in a statement said it has “intensified its defense actions” and boosted its military presence in the region as a result of the dispute.

Essequibo is larger than Greece and rich in minerals. It also gives access to an area of the Atlantic where oil in commercial quantities was discovered in 2015, drawing the attention of Mr. Maduro’s government.

Venezuela’s government promoted the referendum for weeks, framing participation as an act of patriotism, and often conflating it with a show of support for Mr. Maduro. His government held a mock referendum last month, but it did not release participation figures or results.

Venezuela has always considered Essequibo as its own because the region was within its boundaries during the Spanish colonial period, and it has long disputed the border decided by international arbitrators in 1899 when Guyana was still a British colony.

That boundary was decided by arbitrators from Britain, Russia and the United States. The United States represented Venezuela on the panel in part because the Venezuelan government had broken off diplomatic relations with Britain.

Venezuelan officials contend that Americans and Europeans conspired to cheat their country out of the land and argue that a 1966 agreement to resolve the dispute effectively nullified the original arbitration.

Guyana, the only English-speaking country in South America, maintains the initial accord is legal and binding and asked the International Court of Justice in 2018 to rule it as such, but a ruling is years away.

Voters on Sunday will have to answer whether they “agree to reject by all means, in accordance with the law,” the 1899 boundary and whether they support the 1966 agreement “as the only valid legal instrument” to reach a solution.

Mr. Maduro and his allies are urging voters to answer “yes” to all five questions in the referendum.